Math CentralQuandaries & Queries


Question from Harry, a student:

Hey Math Central, I came across your website and im in need of help on my maths c assignment. I have to convert base 3 to 5 without converting back to ten. I heard that you can use patterns in 3 and 5 to make an equation but im not sure how to and i also heard you can use logarithms but i dont know how to use those so im kinda stumped.
Any help given would be awesome,


The simplest way to do it is this. First make a small table of powers of 5 in base 3.

1 = 1 (base 3)
5 = 12 (base 3)
25 = 221 (base 3)
125 = 11122 (base 3)

Now using division or repeated subtraction do the conversion.

EG: 1000 (base 3 [=27 base ten]) is between 221 and 1112.
Subtract 221 once,
remainder is 2: five-squareds digit is 1

This is not between 12 and 221:
fives digit is 0
It is between 1 and 12;
subtract twice, units digit is 2

1000 (base 3) = 102 (base 5)

Good Hunting!

About Math Central


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.
Quandaries & Queries page Home page University of Regina PIMS